Neutron Time-of-Flight Spectroscopy · The neutron time-of-flight technique has a long and distinguished history. In 1935, only 3 years ... used by Enrico Fermi and his collaborators

Volume 98, Number 1, January-February 1993

Journal of Research of the National Institute of Standards and Technology

[J. Res. Natl. Inst. Stand. Technol. 98, 71 (1993)]

Neutron Time-of-Flight Spectroscopy

Volume 98 Number 1 January-February 1993

John R. D. Copley and The time-of-flight technique is employed cussed. We also present brief descrip-Terrence J. Udovic in two of the instruments at the NIST tions of the CNRF time-of-flight in-

Cold Neutron Research Facility (CNRF). struments, including their modi operandiA pulsed monochromatic beam strikes and some of their more pertinent para-

National Institute of Standards the sample, and the energies of scattered meters and performance characteristics.

and Technology, neutrons are determined from their times- Key words: diffusion; hydrogen in

Gaithersburg, MD 20899 of-flight to an array of detectors. The time- metals; inelastic scattering; neutronof-flight method may be used in a variety choppers; neutron inelastic scattering;of types of experiments such as studies of quasielastic neutron scattering; time-of-vibrational and magnetic excitations, tun- flight spectroscopy; tunneling spec-neling spectroscopy, and quasielastic scat- troscopy; vibrational spectroscopy.tering studies of diffusional behavior;several examples of experiments are dis- Accepted: July 22, 1992

1. Introduction

The neutron time-of-flight technique has a longand distinguished history. In 1935, only 3 yearsafter the discovery of the neutron, a pair of rotat-ing disks was used to "prove by direct measure-ment that many of the slow neutrons [from a mod-erated Rn-Be source] are in the thermal velocityrange" [1]. With the advent of the nuclear reactor(in 1942), more difficult measurements becamepossible, and a very different type of chopper wasused by Enrico Fermi and his collaborators to de-termine the energy dependence of the absorptioncross section of boron [2]. By 1960 relatively so-phisticated phased chopper machines were beingused to measure the scattering properties of mate-rials such as water and polyethylene [3]. Much ofthe motivation for these experiments reflected theneed for "scattering law" data for numerical calcu-lations of the behavior of neutrons within nuclearreactors. Since the mid-sixties the emphasis hassteadily shifted to the study of more and more com-plicated materials, and several kinds of time-of-flight instruments have been developed in order tomake possible many different types of experiments[4,5].

The time-of-flight (TOF) method complementsthe triple-axis spectrometer (TAS) techniquewhich is discussed elsewhere in this volume [6].The TAS is ideally (but by no means only) suitedto the study of excitations in oriented samples atspecific points in (Quw) phase space. On the otherhand TOF instruments may be used to explorerather large regions of phase space because manydetectors simultaneously collect neutrons over awide range of values of the scattered energy. Theprice paid for the much larger phase space volumeis that the intensity on the sample is significantlyreduced because the incident beam is pulsed. Inanother respect the TOF method complements thevery high resolution backscattering and neutronspin echo techniques [7].

In Sec. 2 we present the basic principle of atime-of-flight measurement at a reactor-basedspectrometer. We then illustrate several uses of thetechnique, describing a variety of applications indifferent fields of research. In Secs. 4 and 5 wedescribe the more important features of the TOFinstruments at the CNRF, aspects of their

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anticipated performance, the concept of accessibleregions in (Q,w) space, and resolution and inten-sity considerations. In Appendix A we presentimportant relationships between the wave- andparticle-like properties of a thermal neutron. InAppendix B we discuss the functions of the variouschoppers in a multiple disk chopper TOF spec-trometer.

2. The Time-of-Flight TechniqueA simple time-of-flight spectrometer is illus-

trated in Fig. 1. Neutrons from the reactor strike acrystal monochromator which is oriented at angleOM to the initial beam direction. Those with wave-length

Ao=2dM sinOM,

measurements are made for the sample of interestand an "empty container," and in some cases addi-tional runs must be performed in order to establishcalibration constants for the data analysis. The con-version of the raw data to a differential scatteringcross section is straightforward, but corrections forinstrumental resolution, and for effects [4] such asmultiple scattering, sometimes complicate the datareduction procedure. The final result is the scatter-ing function S(Q,o) (cf. Ref. [8]) within the regionof (Qu,) phase space accessed in the experiment.The latter concept is discussed in Sec. 5.1.

D

(1)

where dM is the spacing between reflecting planes inthe monochromator, are Bragg reflected in the di-rection of the sample. The monochromatic beam,characterized by its energy Eo and wave vector ko, isthen pulsed by a chopper placed at a known dis-tance Lcs from the sample. An array of detectors isarranged at a known fixed distance LSD from thesample, and scattered neutrons arrive at the detec-tors at times determined by their scattered energiesE. The time-of-flight of a neutron from the chopperto one of the detectors is simply

tCD tcs + tSD = To Lcs + TLSD. (2)

Here tcs and tSD are the times-of-flight of the neu-tron from chopper to sample and from sample todetector, respectively, and To and T are the recipro-cal velocities of the neutron before and after scat-tering, respectively; relationships between A, T, k,and E are given in Appendix A. From Eq. (2) it isclear that T, E, and the energy transfer

hwo =Eo-E, (3)

may be determined from tCD if Ao is known. Giventhe angle between the incident and scattered neu-tron wave-vectors, i.e., the scattering angle 4, thewave-vector transfer

Q=ko-k (4)is readily calculated. The vast majority of samplesstudied by TOF spectroscopy have no preferred ori-entation, so that all that generally matters is themagnitude of Q. We shall ignore the vector charac-ter of Q in the remainder of this paper.

The basic quantity which is measured in a TOFexperiment is a set of intensities I(O),tj) for nD de-tectors located at scattering angles A. (i =1,2..nD),

in n, time channels centered at times tj = 1,2,. .n,)

relative to an appropriate start time. Typically,

- l11CS . L'*<.,

Fig. 1. Schematic plan view of a simple time-of-flight spectrom-eter. The letters R, M, C, S, and D denote the reactor,monochromator, chopper, sample and detectors, respectively.Important distances are indicated. In practice, the slots in the(Fermi) chopper are curved in order to optimize its transmission.

3. Applications

The utility of TOF spectroscopy stems from itsability to access a region of (Q,w)) phase spacewhich is at the same time important to an under-standing of the chemical physics of condensedphase materials, yet difficult to explore by otherspectroscopic techniques. Applications of TOFspectroscopy are diverse and numerous (see, e.g.,Refs. [4] and [9]). They include investigations of (i)vibrational and magnetic excitations by inelasticscattering, (ii) intermolecular potentials by tunnel-ing spectroscopy, and (iii) translational and reorien-tational dynamics by quasielastic neutron scattering(QENS). The theoretical framework behind suchinvestigations is summarized elsewhere in this issue[7,8]. The following examples elaborate on these ar-eas and provide a flavor of the benefits of TOFspectroscopy.

3.1 Inelastic Scattering

The TOF technique is useful as a low energy vi-brational spectroscopic probe of condensed phasematerials, particularly those in which hydrogen mo-tions are important, due to the relatively high inco-herent scattering cross section of hydrogen [4,8,10].The energy range accessible in TOF measurementsmakes the technique complementary to other vibra-tional probes which access both higher and lowerenergy ranges. For example, Fig. 2 shows TOF

72



spectra for trimethylsilyl [(CH3)3Si-, TMS] adsor-bates bonded to silica via surface oxygens [11]. Anenergy loss feature at -2.5 meV at 4 K shows upas both energy loss and energy gain features at 10K due to increasing population of the 2.5 meVlevel above the ground state as the temperature israised. This low energy feature is assigned to thetorsional vibration of the entire trimethylsilyl grouparound the O-Si axis, since the relatively large mo-ment of inertia of this group places the torsionalmode in this energy range. The -2.5 meV vibra-tional feature is outside the higher energy (15-250meV) window of a triple-axis/Be-filter spectrome-ter [10] which was used to measure the other TMSnormal-mode vibrational energies.

The complementarity of TOF measurementswith other vibrational probes is further illustratedin an investigation of the vibrational dynamics offractal silica aerogels by neutron TOF, backscatter-ing, and spin-echo techniques in conjunction withRaman spectroscopy [12]. Real fractal solids con-sist of particles, of typical size a, distributed infractal fashion up to a correlation length 6, beyondwhich the materials are homogeneous. Threeregimes can be identified for vibrations of charac-teristic length e, namely phonons (e> eac), fractons

1

a,a)

IL

0

C,,z

uLJ

0

10i

,C-2

10-3

-410

0.1

0

-~10KQ) f *~~~~~~

4K

-12 -6 0 6 12Energy Transfer (meV)

Fig. 2. Low-energy (Eo= 13.8 meV) inelastic TOF spectra for

trimethylsilyl adsorbates on silica at 4 and 10 K. Positive energytransfers correspond to neutron energy loss [11].

( > e >a), and particle modes (a > e), where tar

is the acoustical correlation length. Figure 3

1 10 100 1000 10000

FREQUENCY (GHz)

Fig. 3. The density of states (DOS) of a silica aerogel synthesized by hydrolysis

of tetramethoxysilane without the addition of ammonia to the reaction water. The

open circles are TOF measurements at 160 K using 8 A incident neutrons. The

dotted curve indicates the DOS that fits neutron spin-echo data. The solid line is

a fit to neutron backscattering data and is extrapolated as shown by the dashes

throughout the high-frequency fracton region. The dashed lines indicate the

asymptotic phonon as well as the independent bend and stretch contributions

[12].

73

-1



displays the density of states of a silica aerogelsynthesized by hydrolysis of tetramethoxysilanewithout the addition of ammonia to the reactionwater. The TOF data, which cover the high fre-quency region, were derived from the purely inco-herent contribution using the difference betweensignals measured on two samples: one with protonsattached to the silica network and the other withthe protons substituted by deuterons. The combi-nation of different neutron scattering measure-ments illustrates the three regimes (note that 1GHz=4.1357 peV): phonons at low frequencies,( < 0.7 GHz), fractons at medium frequencies (0.7-250 GHz), and particle modes at higher frequen-cies ( > 250 GHz). In addition, the data suggest twodistinct elastic r6gimes in the fracton range as pre-viously predicted [13], associated with bending atsmaller scales and stretching at larger scales.Greatly different Debye-Waller factors were foundin the two regimes, enabling them to be unambigu-ously distinguished in the neutron spectra.

Time-of-flight instruments, unlike crystal spec-trometers [6], do not readily lend themselves to in-vestigations at constant wave-vector transfer Q. Onthe other hand the broad Q range available at agiven energy transfer, using a multidetector TOFspectrometer, is well-suited to the study of disper-sionless phenomena such as crystal-field excitations[14]. This is exemplified in Fig. 4, which illustratesthe crystal field transitions (at 3.52 and 6.65 meV at10 K) of the rare earth ion Ho"+ in the cubicHeusler alloy HoPd2 Sn. The neutron energy loss in-tensity for each transition decreases with increasingtemperature as expected due to the depopulation ofthe crystal-field ground state. At elevated tempera-tures, when the higher energy crystal-field levels be-come thermally populated (e.g., at T = 23 and40 K), an additional transition at - 3.5 meV on theneutron energy gain side is also evident. At eachtemperature, no variation of the excitation energieswas observed from detector to detector indicatingthat the transitions were indeed dispersionless. Thispermitted an improvement of the statistics by sum-ming many detectors over a broad Q range.

Figure 5 illustrates the dispersionless, first ex-cited level, magnetic-pair scattering energy(ENN = 8.19 ± 0.05 meV) in both energy loss (at17 K) and energy gain (at 100 K) for nearest-neigh-bor (NN) Co2" ions in the II-VI diluted magneticsemiconductor ZnO.94 Co0.6S [15]. The interactionbetween the two NN Co2" ions can be treated, to afirst approximation, as a Heisenberg-type exchangefor a pair of Si= Si= 3/2 spins described by theHamiltonian H = 2JNNSi 'Sj. Thus ENN becomes a

direct measure of the antiferromagnetic exchangeconstant JNN (where ENN = 2

JNN), yielding a value ofJNN = 4.10 ± 0.03 meV, in good agreement with theresult obtained from magnetic susceptibility studies[16]. In this alloy, the magnetic Co2" ions are ran-domly distributed over a face-centered-cubic cationsublattice. Hence, 48% of the ions are singlets,24% are members of NN pairs, 4% belong to tri-ads, and the remainder to larger clusters. Since thesinglet Co2" ions only possess excited state levelswith much higher transition energies outside the

600

500

400

300

200

zD00Liiz

100

0

100

0

100

0

100

0 . .. ................I.....4......I.. .I.. .I.. 1---6.0 -3.5 -1.0 1.5 40 6.5 9.0

ENERGY (meV)

Fig. 4. Elastic and inelastic scattering observed in a powdersample of HoPd2 Sn using the TOF technique with incident en-ergy 13.8 meV. To improve the statistics, the spectra shownwere obtained by summing over data acquired in 60 detectorsspanning a Q range from 0.48 to 3.85 A-'. At 23 and 40 K,transitions from higher-energy to lower-energy levels are alsoevident in neutron-energy-gain (E <0) [14].

74



I---,

.

10

Lt

I e

V)4--

-20 -15 -10 -5 6 8 10

Energy (meV)

Fig. 5. Examples of inelastic TOF spectra (Eo= 13.8 meV) for ZnO.94CoO.(6S. The rightpanel shows the neutron energy-loss side of the spectrum obtained at 17 K with a fittedGaussian line shape. The left panel shows energy-gain spectra at 100 K obtained by sum-ming the counts from all detectors, from the "high-Q" detectors, and from the "low-Q"detectors. The curves are guides to the eye [15].

relevant measurement range, Co-Co pair scatteringis the dominant magnetic inelastic effect in this al-loy composition region. Yet its intensity is expectedto be relatively weak because the pairs constituteonly a small fraction of the total number of atomsin the sample. Since pair scattering energies aredispersionless, the ability to analyze the 100 K TOFspectra as a function of the Q range is useful inorder to corroborate evidence that the broad fea-ture at -11 meV is due to Q 2-dependent phononscattering, rather than to magnetic-pair scattering.

3.2 Tunneling Spectroscopy

Time-of-flight spectroscopy is a useful probe ofintermolecular potentials through characterizationof tunneling transitions in condensed-phase materi-als. For example, Fig. 6 is a TOF spectrum illustrat-ing the rotational tunnel splitting of the librational

ground state of molecular hydrogen adsorbed in thecavities of partially cobalt-exchanged type A zeolite(Co4 .UNa3 .M-A) [17]. The assignment of the 3.8 meVneutron energy gain and energy loss features to thelibrational ground-state splitting (i.e., between theJ = 0 (para H2) and J=1 (ortho H2) rotationalstates) is unambiguous since the expected intensityratio between energy gain and energy loss processeswould be about 1:40 at 12 K for a translational exci-tation. This assignment, in conjunction with excita-tion data at higher energy transfer determinedusing a triple-axis spectrometer, is in good agree-ment with a model for the H2 molecules in a twofoldcosine potential with two degrees of rotational free-dom. The model implies that the H2 molecules arebound end-on to the cobalt cations, and perform1800 reorientations with a barrier of 55-68 meV.

75



00

0

z

-12 -6 0 6 12Energy (meV)

Fig. 6. TOF spectrum (Eo= 14.8 meV) of 0.5 molecules ofhydrogen per supercage adsorbed on Co4.,Na3 .8-A zeolite at 12K. The spectrum of the dehydrated zeolite has been subtractedfrom the data. Positive energy represents neutron energy loss[17].

The advent of high resolution TOF (andbackscattering [7]) spectrometers, over the past twodecades, has provided the ability to measure muchlower energy tunneling transitions of condensedmolecules and atoms. This is exemplified by thestudy of quantum states, transitions and interac-tions in the solid methanes [18]. Figure 7 illustratesTOF tunneling spectra for phase II CH4 at low tem-peratures. In this cubic phase (space group Fm3c),two of the eight molecules in the unit cell are essen-tially freely rotating, while the other six moleculesare in sites of (42m) symmetry, are orientationallyordered, and undergo tunneling. There are threecorresponding tunneling states for a tetrahedralmolecule or group experiencing a hindering poten-tial in a tetrahedral site symmetry: a singlet groundstate (A) and triply and doubly degenerate levels (Tand E). Neutron induced transitions from A to Estates are not observed since this requires a nuclearspin change from I = 2 to I = 0, which cannot becaused by a spin 1/2 particle. The 0.2 K spectrumshows an almost complete occupation of the Aground state species, which allows observation ofA - T transitions only. As the temperature is raised

Neutron Energy Gain (peV)

(b)

15

A-T

C

1 0

-05

0 -.

-200 -100 0 100 200Neutron Energy Gain (peV)

Fig. 7. TOF spectra for 13 A neutrons scattered by CH4 (phaseII) at sample and spin temperatures of (a) <0.2 K and (b) 5K. The A-T and E-T transitions are labelled in (b) [18].

both T and E states become populated, allowingobservation of A-T and E-T transitions by bothneutron energy loss and energy gain scattering. Anexcellent fit to the observed temperature-dependent widths and energies of these transitions(Fig. 8) assumes a continuously changing local po-tential, reflecting the changing mixture of spinstates with temperature. The highest A-T energy(163.5 pteV) observed at the lowest temperatures( <0.5 K) reflects the potential for A level speciessurrounded by like species. Decreasing frequencies

76



(and concomitant increasing linewidths), observedwith increasing temperature, indicate an increasingadmixture of T and E species, increasing the aver-age barrier height of the ordered CH4 molecules inthe unit cell.

2 1-- Temperature (K)

Fig. 8. Energy of the A-T transition peak as a function of theconcentration of the A spin species. The straight line representsa fit with the model of inhomogeneous broadening due to achanging mixture of spin states [18].

3.3 Quasielastic Neutron Scattering (QENS)

Time-of-flight spectroscopy is well-suited toprobing the translational and reorientationaldynamics of atoms and molecules in condensedphase materials, particularly those with importanthydrogen motions, via the Q - and T-dependence ofthe associated quasielastic neutron scattering. Forinstance, the localized motion of hydrogen in ana-ScHo.16 solid solution has been investigated byQENS using TOF techniques [19]. The hydrogenatoms in this system are restricted to pairs ofnearest-neighbor tetrahedral (t) sites betweenmetal atoms along the c-axis. All scattering spectrawere fit with an empirical two-component functioncomprising an elastic term described by theresolution function of the spectrometer and a reso-lution-broadened Lorentzian quasielastic term.Throughout the measurements, the invariance ofthe quasielastic linewidth F with Q corroboratedthe localized nature of the hopping motions. A

hopping distance of 0.10 nm (1 A) was abstractedfrom the data on the elastic incoherent structurefactor (EISF) as a function of Q, consistent withthe known nearest-neighbor t-t distance in thismaterial. Figure 9 illustrates quasielastic scatteringspectra for a-ScHo.16 at several temperatures; Fig.10 is a plot of F vs T. The data show hydrogenhopping rates between t sites exceeding -7 x 1010s- at all temperatures, indicating very rapidmotion compared with the bulk diffusion rate inthese systems. The apparent hopping rate increasesto 1012 s-' at 10 K after passing through a minimumat - 100 K. This remarkable upturn of F below theminimum is approximately proportional to T` inthe range shown and is explained in terms ofKondo's [20] prediction of nonadiabatic effects ofthe coupling of the metal conduction electrons tothe protons.

5

4

3

2

Co

=3

Co

Ci)

0

0.5

00.5

00.2

0

0.1

To-1 -0.5 0 0.5 1

Energy (meV)

Fig. 9. Quasielastic neutron scattering spectra for a-ScH 1.16 atseveral temperatures at 70 pLeV FWHM elastic energy resolu-tion. The solid lines are the results of least-squares fits to thedata; the dotted lines represent the Lorentzian quasielasticcomponent. The increase in the quasielastic linewidth at lowtemperature is illustrated in the 50 K spectrum, where thelength of the horizontal bar is equal to the width of the 70 KLorentzian component [19].

77

1

-



1 10 100

slower for methane in the zeolite than in phy-sisorbed layers or in the solid phase.

1000T (K)

Fig. 10. Fitted Lorentzian linewidths (FWHM) for a-ScH0 1 6.The solid line is the fit to the data below 100 K, assuming elec-tronically induced linewidth broadening with decreasing tem-perature as described in the text [19].

A similar Kondo effect was observed below -70K in the quasielastic scattering from hydrogentrapped by oxygen impurities in Nb (i.e., Nb(OH).,1.5 x 10-4<x 1.1 x 10-2) [21,22]. In particular, thehydrogens are trapped at weakly distorted tetrahe-dral sites in the body-centered-cubic lattice gener-ated by the presence of oxygen defects at octahedralinterstitial sites. Local diffusion of hydrogen occursbetween at least two nearest-neighbor tetrahedraltrap sites. Above -70 K, the diffusion is dominatedby the interaction with phonons. Below 5 K, well-defined tunneling eigenstates exist due to delocal-ization of the H between trap sites. Figure 11 showsa narrow inelastic tunneling transition at the lowestmeasured hydrogen concentration (x = 1.5 x10-4),which changes into a broad peak at higher concen-trations due to increasingly strong interactions be-tween defects.

The ability of TOF techniques to probe molecu-lar dynamics on an atomic scale is further exempli-fied by QENS investigations of the translationaland rotational motions of hydrocarbons adsorbed inzeolites, namely benzene in Na-mordenite [23] andmethane in Na-ZSM-5 [24]. Figure 12 compares theEISF data for benzene in Na-mordenite with vari-ous theoretical models for the benzene reorienta-tion. The data suggest that the benzene molecules,likely adsorbed by the Na cations via cation interac-tion with the 7r-electrons, undergo discrete uniaxialrotational jumps of 2ir/6. In contrast, methane inNa-ZSM-5 is found to undergo isotropic rotationaldiffusion. In this model, methane molecules are as-sumed to perform continuous small-angle rotationsand therefore have no preferred orientation inspace. This rotational motion is found to be much

W

C

a,

C

CI)

4'0

C

3

0W

-0.5Energy transfer (meV)

Fig. 11. TOF tunneling spectra measured (in neutron energyloss) at three OH concentrations in Nb(OH). at 1.5 K Elasticenergy resolution was 55 pLeV FWHM [21].

78

1000

100a)

L.

S

0

X~~~~~ *I . I . ... -.. I . II. 1.... . .10

or-1 0



LI

0.5

0 0.5 1.0 1.5

Fig. 12. Elastic incoherent structure factors (EISFs) of ben-zene adsorbed in Na-mordenite zeolite as a function of scatter-ing vector Q. Open circles represent the experimental data.Theoretical EISFs are shown for rotational diffusion (brokenline), for uniaxial rotations of 27r/6 (full line) and for uniaxialrotations of 27r/3 (dotted line) [23].

The translational diffusion behavior also differsbetween the two hydrocarbon/zeolite systems. Forbenzene in Na-mordenite, the benzene-Na bondingis weak, and the elastic peak width possesses a Q-dependence, implying that the benzene moleculesfollow Fick's law of continuous translational diffu-sion, characteristic of diffusion in a liquid, ratherthan a jump diffusion mechanism. The translationaldiffusion coefficient was found to be 6.7 x 10' cm2

s'- at 300 K. In contrast, for methane in Na-ZSM-5,the broadening of the elastic peak versus Q2 devi-ates from a straight line (see Fig. 13) so that, on anatomic scale, the motion of methane is not simplyFickian. Instead the data agree with a model fortranslational diffusion which assumes jump diffu-sion with a Gaussian distribution of jump lengths.The physical interpretation of the model is thatmethane can perform small jumps inside the zeolitechannels, but larger jump distances across the chan-nel intersections are also possible. After a largenumber of jumps, Fickian diffusion can be ob-served. The diffusion coefficients for long rangetranslational motion (2.7 x 10- and 5.5 x 10- cm2

s at 200 and 250 K, respectively), determinedfrom asymptotic values of the broadening at low Q,do not vary much with methane loading.

30

Z-

:2

3.

20-

10-

40-

30-

20-

.

(a)

(b)

0 0.2 0.4 0.6 0.8a 2 (A-2)

Fig. 13. Broadening of the elastic peak as a function of Q2 formethane in ZSM-5 zeolite at 250 K: (a) 1.5 molecules and (b) 2.8molecules per unit cell [24].

4. Time-of-Flight Instruments at the ColdNeutron Research Facility

Two time-of-flight spectrometers are planned forthe guide hall of the CNRF. The first of these in-struments, which is primarily designed for mediumresolution applications, is a modified version of thetype of instrument depicted in Fig. 1; it is located onguide NG-6, as shown in Fig. 7 of Ref. [25]. We callit the Fermi Chopper Spectrometer (FCS).

The second instrument, to be located at guideNG-4, uses a number of disk choppers tomonochromate and pulse the incident beam; it is in-tended for high resolution measurements but mayalso be operated with relaxed resolution when re-quired. We call it the Disk Chopper Spectrometer(DCS).

79



4.1. The Fermi Chopper Spectrometer

The Fermi Chopper Spectrometer is illustratedschematically in Fig. 14. Detailed specifications arelisted in Table 1. The incident beam wavelength(0.23-0.61 nm) is determined using a doublemonochromator. The principle of this device issimilar to that of a single monochromator, but animportant advantage is that the selected neutronwavelength can be changed without having to ro-tate virtually the entire spectrometer about themonochromator axis. This significantly simplifiesthe design of the instrument. The monochromatorsare made of individually aligned pyrolytic graphite(PG(002)) crystals. A 60' Soller collimator is lo-cated between the monochromators. The firstmonochromator is flat, whereas the secondmonochromator is vertically curved in order tofocus intensity at the sample position. Verticalfocussing is optimized when the vertical mosaicspread is minimized, yet this same mosaic spread inthe horizontal direction would lead to an unneces-sarily small wavelength spread and a consequentdecreased intensity on the sample. Hence eachmonochromator is made of two layers of crystals,each layer possessing a 25' mosaic, but staggeredhorizontally with 25' angular offset. This effectivelyyields a more desirable anisotropic mosaic distribu-tion, 25' vertically and 50' horizontally.

The neutron beam leaving the second monochro-mator is filtered, using pyrolytic graphite or liquidnitrogen-cooled beryllium (see Table 1), in order toremove Bragg (A/n) (where n is an integer >1)order contamination (cf. [6]), as well as epithermalneutrons. It is then pulsed using a "Fermi chop-per" [2]. This is a device which spins about a verti-cal axis (normal to the direction of the beam), andis fitted with a set of curved slots. The curvature ofthe slots and the speed of the chopper determinethe optimum transmitted wavelength of the chop-per [5]. Two slot packages are available, corre-sponding to optimum transmitted wavelengths of0.4 and 0.15 nm, respectively, at close to the maxi-mum chopper speed.

The sample chamber can accommodate a widevariety of cryostats and furnaces. An oscillating ra-dial collimator between the sample and the detec-tors blocks most of the scattering from materialcomponents which surround the sample (e.g., heatshields of cryostats). The evacuated sample-to-detector flight path contains an array of 'Heneutron detectors covering a scattering range of5°-4400. Signals from the detectors are amplified,shaped and filtered, and then fed to a time-of-flight encoder and CAMAC-based histogrammingmemory. The contents of this module are periodi-cally transferred to a microVax computer for sub-sequent analysis.

G

Fig. 14. Simplified plan view of the Fermi chopper spectrometer. The letters G, F, C, S,and D denote the guide, filter, chopper, sample and detectors respectively; Ml and M2 arethe monochromator crystals and RC is the (oscillating) radial collimator. Incident wave-lengths between 0.23 and 0.61 nm are obtained by modifying the Bragg diffraction angle ofthe double monochromator, as suggested by the dashed lines in the figure. The guide iscontinued to additional instruments downstream.

80



Table 1. Specifications and anticipated performancedetails are given in the text

SpecificationsGuide cross section (height x width):Maximum beam size (height x width):Monochromators (double):1st Monochromator (height X width/type):2nd Monochromator (height x width/type):Monochromator mosaic (vertical/horizontal):Intermonochromator collimation:Beam filters (thickness/type/temperature):

Fermi chopper details (2 slit packages)Blade curvature radius:Rotor radius:Slot width:Beam window (height x width):Optimum chopper speed:Sample -detector distance:Scattering angle range:

Post-Sample radial collimation (oscillating)Blade separation:Inner/Outer radius:

Detectors (cylindrical, 3He-filled)Fill pressure:Diameter:Angular separation:Quantity/Active height:

Incident wavelength range:Incident energy range:Elastic momentum transfer range:

Anticipated performanceFluence rate on sample:

Elastic energy resolution:

Q Resolution:

of the Fermi Chopper Spectrometer. Additional

150 x 60 mm100 x 25 mmPyrolytic graphite PG(002)160 x 100 mm/flat184 x 100 mm/vertically focussing25'/50'60'152 mm/Be/77 K for A > 0.4 nm38 mm/PG/296 K for select A < 0.4 nm

Package 1 Package 2389.0 mm 581.4 mm26.9 mm 25.6 mm0.635 mm 0.635 mm100 x 25 mm 100 x 25 mm80.93/A(nm)Hz 54.15/A(nm) Hz2.286 m50<4 <1400

30203/305 mm

0.4 MPa25 mm1.273°12/229 mm for 50< 20 < 20088/457 mm for 200<20<14000.23 < AO < 0.61 nm ( + 2 for PG(004))15.5 >E 0 >2.2 meV (x4 for PG(004))1 <Q <50 nm-I ( x 2 for PG(004))

- 1 X 108 n/m2/s at A = 0.24 nm- 1.2 x 108 n/m2/s at A = 0.40 nm40 geV at A =0.60 nm150 ,ueV at A = 0.40 nm600 ,eV at A =0.24 nmAQ/Q < 3%

4.2 Disk Chopper Spectrometer

The Disk Chopper Spectrometer is illustratedschematically in Fig. 15. The "front end" comprisesa novel neutron filter followed by a total of sevendisk choppers which collectively produce a clean,usable, pulsed, monochromatic neutron beam at thesample position. The purpose of each of these chop-pers is explained in Appendix B. The multichopperdesign (Fig. 16) allows the user a wide and continu-ous choice of wavelengths, basically constrained bythe available spectrum of neutrons in the guide; achange in wavelength is achieved by changing thephase relationship between the disks.

In general the instrumental resolution may bevaried (at fixed wavelength) either by changing thespeed of the choppers or by changing the width ofthe beam. It is actually preferable, for reasons dis-cussed in Appendix B, to change the width of thebeam keeping the choppers spinning as fast as pos-sible consistent with the desired resolution and withsafe operating procedures. To optimize perfor-mance this implies changes both in the widths of theslots in the disks and in the width of the guide [26].The practical realization of this option requiressome explanation.

81



G -

Mcc-IPC

IALI'

FRC

ORC

Fig. 15. Simplified plan view of the disk chopper spectrometer.The upper diagram shows the overall setup of the instrumentincluding cold source (CS), filter (F), and guide (G). The lowerdiagram shows the choppers, the sample position (S), and thedetectors (D); PC, ORC, FRC, and MC denote pulsing, orderremoval, frame removal, and monochromating choppers,respectively. The width of the guide, the separation betweenclosely spaced choppers, and the angle between initial and finalguide sections, have been exaggerated for clarity. The filter is atapered section of guide, -7 m long, that redirects slow neu-trons (through 0.25°) whereas fast neutrons and y rays areremoved from the beam because they are not reflected. It islocated within the wall between the reactor confinement build-ing and the guide hall.

Monochromating Choppers

Pulsing Choppers

Fig. 16. Simplified view of the choppers and guide for the diskchopper spectrometer. Note that the pulsing and monochromat-ing chopper disks each have three slots (of different sizes fordifferent resolution modes of the instrument) and that the guideis divided into five channels.

Each of the disks in the pulsing and monochro-mating chopper pairs is equipped with three slots ofdifferent width, as shown in Fig. 16. The slots ineach counter-rotating pair are located such that thewidth of the slot presented to the neutron beam canbe changed by grossly changing the relative phasingof the disks. The choice of slot positions is compli-cated because of effects resulting from the smallseparation between the members of a counter-rotating pair [27,28].

The neutron guide for the DCS is of rectangularcross section, 150 mm high and 60 mm wide, until itreaches the filter; thereafter it is 30 mm wide. Afterthe first chopper it is best described as a channeledguide, fitted with internal reflecting plates as shownin the insets to Figs. 15 and 16. Beam-definingmasks limit the number of channels which transmitneutrons, effectively changing the width of theguide. The widths of the channels, and the widths ofthe slots in the disks, have been chosen to optimizeintensity on the sample under each of three distinctresolution conditions at a given wavelength andchopper speed [26]. Typically the overall resolutionwidth doubles, and the intensity on the sample in-creases by about an order of magnitude, in goingfrom high to medium resolution or from medium tolow resolution. The capability to change resolutionat fixed wavelength and fixed chopper speed is onlypossible because we use counter-rotating chopperswith multiple slots [29].

After the final chopper the layout of the instru-ment is not unlike that of the Fermi Chopper Spec-trometer, described in the previous subsection. Thesample chamber is comparable in size and will beevacuated. On the other hand, the flight path be-tween sample and detector will be filled with an in-ert gas in order to reduce scattering, and thedetectors will be mounted externally. An importantdifference is that the distance LSD is significantlylarger (4000 mm), in order to achieve the desiredenergy resolution. For the same reason, the detec-tors will be very thin (-10 mm) in the directiontravelled by the neutrons, but relatively wide (-32mm) in order to capture as many neutrons as possi-ble. They will be rectangular 'He tubes, typically400 mm long, and there will be three detector banksspanning a wide range of scattering angles. Thedata acquisition system will be an expanded andsomewhat more elaborate version of the systemused in the FCS.

Certain specifications of the DCS are listed inTable 2; some of the numbers may be modified asthe design progresses. Figures for the anticipatedintensity on the sample are somewhat speculative,and the reader is cautioned not to take these inten-sities at face value. The Q resolution of the instru-ment will depend on how the detectors aregrouped; the best achievable resolution can be esti-mated from the anticipated resolution in Ao (whichdepends on Ao itself, the speed of the choppers, andthe resolution mode of the choppers), the diver-gence of the incident beam (which depends on Ao),and the angle subtended by a single detector at thesample position.

82



Table 2. Specifications and anticipated performance of the disk chopper spectrometer. Sets of three

quantities within braces refer to the three resolution modes of operation of the instrument, {low,medium, high}, respectively

SpecificationsBeam height at guide exit:Beam width at guide exit:

Disk chopper details:Outside radius:Maximum operating speed:Maximum tip velocity:Pulsing chopper slot widths:Monochromating chopper slot widths:Order removal chopper slot widths:Frame removal chopper slot width:Sample-Detector distance:Anticipated maximum scattering angle:

Detectors (rectangular cross-section, 3He-filled)Fill pressure:Width:Thickness:Active length:Arrangement:Approximate incident wavelength range:Approximate incident energy range:Corresponding elastic Q range:

Anticipated performance(assuming a chopper speed of 20,000 rpm)Fluence rate on sample (Ao = 0.2 nm):

(Ao = 0.4 nm):(Ao=0.6 nm):(Ao = 0.8 nm):

Elastic energy resolution (Ao = 0.2 nm):" " " (Ao= 0.4 nm):

"" (Ao= 0.6 nm):(Ao=0.8 nm):

100 mm{30 mm, 15 mm, 5 mm}

290 mm333 Hz (20,000 rpm)607 m/s{12°, 6.50, 2.6°}{8°, 350, 1.35°}200, 1802004 m1400

0.6 MPa-32 mm-10 mm400 mm3 banks0.2 < A, < 1.5 nm20>Eo>0.36 meV0.5<Q <60 nm '

{45, 10, 2} x 106 n/m2/s

{450, 100, 20) x 106 n/m2/s{220, 50, 10) x 106 n/m2/s{100, 20, 5} x 106 n/m2/s{1300, 650, 270} p1eV{160, 80, 35) peV{50, 25, 12} pLeV{21, 11, 6} peV

5. Experimental Considerations

When planning a time-of-flight experiment theinterplay of resolution and intensity requirementsis an important concern. Generally speaking, in-strumental resolution improves dramatically withincreasing wavelength; for example the energywidth of the elastic scattering approximately variesas the n th power of Eo, where n is about 3. On theother hand the intensity at the sample positiontends to decrease as the incident wavelength is in-creased; for instruments on guide tubes the inten-sity varies as A at long wavelengths. It istherefore necessary to strike a compromise be-tween the conflicting requirements of high intensityand good resolution.

A further disadvantage of long wavelengths isthat an increase in wavelength also reduces the ac-cessible region in (Q,w) space. Generally speakingthe best policy is to use the shortest wavelengthconsistent with the desired instrumental resolution,in order to be able to access as large a region of(Q,ws) space as possible.

5.1 Accessible Regions in (Q,w) Space

In TOF experiments the accessible regiondepends on the choice of incident energy and onthe placement of the detectors. The cosine rule,applied to the vectors Q, ko and k [(cf. Eq. (4)],yields the result

83



Q2 = ko2 + k2 - 2kokcos(). (5)

Converting wave-vectors to energies (see AppendixA), and using Eq. (3), Eq. (5) may be rewritten asfollows:

h 2Q 2/2m =2EM- h -2VEo(Eo-hw) cos(qS). (6)

In Fig. 17 we show accessible regions for twochoices of the incident energy. Detectors are as-sumed to fill the angular range from 50 to 140°.

The accessible region gets smaller as Eo is de-creased. In particular the accessible range of Q forelastic scattering (hw = 0) is reduced since in thiscase Eq. (6) simplifies to the well-known (Bragg)relationship

Q =2ko sin(k/2). (7)

and the chopper. The chopper contribution is inde-pendent of distance but the wavelength spread fromthe monochromator translates into a time spreadwhich increases with distance. The net result is thatthe width of the time distribution in the unscatteredbeam, at a point distantx from the chopper, may bewritten as follows:

(8)

where or, measures the burst time of the chopperand A, is the spread in the reciprocal velocity distri-bution of neutrons in the beam.

The time distribution for a two-chopper spec-trometer may be similarly written [30]. In this casethe time spread is an appropriate average of theburst times a, and o2 for the two choppers:

A decrease in Eo also means a proportionate reduc-tion in the maximum possible energy transfer inneutron energy loss. The improved resolution thatresults as Eo is decreased, i.e., as Au is increased, isa direct consequence of the contraction in accessi-ble (Q,w) space.

-6 -4 -2 0 2 (meV)

Fig. 17. Plots of the accessible region in (Q,co) space forneutrons of wavelength 5 and 10 A (energy 3.272 and 0.818 meV,respectively). The minimum and maximum scattering angles are50 and 1400. There is no (theoretical) limit to the energy transferin neutron energy gain.

5.2 Resolution and Intensity

An important contribution to the overall energyresolution of a TOF spectrometer arises from thespread in the time distribution of neutrons in theincident beam.

In the FCS there are two independent sources ofincident beam time spread: the monochromator

2 = 2 O22/(O,2 + (72). (9)

The reciprocal velocity spread o,. is given by

=(a2 = + 0J2)/L, 22 (10)

where L12 is the distance between the two choppers,and the distance x is measured from an "effectivechopping point" which is located between the chop-pers at a distance

L1o=L 12 £72/(a72+ £22) (11)

from the first chopper. These expressions may beused to calculate the time distribution in the inci-dent beam of the DCS.

Important additional contributions to the overallenergy resolution of a TOF spectrometer stem fromflight path uncertainties due to the size of the sam-ple and the geometry of the detectors [5].

The count-rate in a TOF experiment is deter-mined by the intensity of neutrons at the sample po-sition, the scattering properties of the sample, andthe detecting efficiency of the array of detectors. Tosome extent the individual experimenter can selectthe scattering properties of the sample such as itssize and shape, and how it is contained. The effi-ciency of the detector array can generally be in-creased, without degrading resolution, simply bypurchasing more detectors; thus it largely dependson the available budget..The principal challenge indesigning a TOF spectrometer is therefore to opti-mize the "front end" of the instrument, and indeedconsiderable efforts have been devoted to this taskfor both of the CNRF spectrometers.

84

0,2(X) = of 2 +x2 O"r 2,



6. Concluding RemarksThe time-of-flight spectrometers at the CNRF

are the only instruments of their type on the NorthAmerican continent. Once operational, we expectthat they will fill a significant gap in the arsenal ofneutron inelastic scattering instruments availableto the scientific community. We look forward to avariety of collaborations and interactions with sci-entists wishing to use these instruments.

7. Appendix A

A thermal neutron has energy E, wave-vector k,wavelength A, velocity v, and reciprocal velocity T.

These quantities are related as follows:

E (meV) = (h 2/8ir2m )k2 =0.020721 [k (nm 1)]2 (Al)

=h 2/2mA2 _0.81804/[A (nm)] 2

=mv 2 /2=5.2270[v(mm us'L)]2

=m/2T 2 =5.2270/[k(ps mm-')] 2 .

energies. These neutrons have different speeds andtherefore arrive at the monochromating chopper atmany different times. The phasing of the mono-chromating chopper is chosen to transmit neutronsof the desired energy. The operation of this systemcan be represented in a distance-time (xft) diagramas shown in Fig. 19(a).

4

(a)

(A2)

(A3)

(A4)(b)

Furthermore

A(nm)=h/mv= 0.39560/[v(mm ps-')],

and

(AM)

(c)

k(nm-') = 2mnv/h =15.8825[v(mm pus')]. (A6)

In these equations m is the mass of the neutronand h is Planck's constant; values of m and h aretaken from Ref. [31].

Useful conversion factors relating different unitsof energy may also be found in Ref. [31]. Two ofthe most commonly employed conversions are thefollowing:

1 meV=8.0655 cm-'

=0.2418 x 1012 Hz.

8. Appendix B

In the disk chopper spectrometer the functionsof pulser and monochromator are assumed by a setof disk choppers which rotate about a common axisparallel to (and some distance above) the directionof the beam. The essential concept can be under-stood by considering the two chopper arrangementillustrated in Fig. 18(a). The pulsing chopper pro-duces short bursts of neutrons of many different

(d)

Fig. 18. Various chopper arrangements of increasing complex-ity. At (a) is shown the bare minimum two chopper arrange-ment. At (b) is shown a system with two counter-rotatingchoppers. Order removal choppers have been added at (c), anda slow-moving frame removal chopper is included at (d). Thesymbols 1, 2, 3, and 4 label choppers and chopper pairs.

Each of the principal choppers in the DCS isactually a counter-rotating pair of disks, as shownin Fig. 18(b). The effective chopping speed for sucha device is double that of a single disk which ro-tates at the same speed as one of the members ofthe counter-rotating pair [32]. It follows that theintensity per pulse is doubled at constant resolu-tion. This can be understood by considering sys-tems such as the one shown in Fig. 20(a). The burst

85



time of the illustrated system is simply At= (w/u)whereas the transmitted intensity per pulse, Ip, isproportional to (w2Iu), where w is the width of the

- -- - - -slot and the guide, and u is the chopping speed; thetime dependence of the intensity is illustrated inFig. 20(b). Clearly

- L

IPOCU(At)2

xl --,-----<' i--- --- ,- r a -,1T

(c)S4

x2 2

(d)

(e)

-*t

---- -,- - - - --,,

-77

-*~ t

X 4

Xl32

1

n

. ,, ,, 4, , A. , A. , A. , , ,

,/ ,, , ., _ ; _, at-_ ,jR - c c,-, _- -r; ' _ 7, z _ X, - _ _ s SS _ _ I,, _ _ to , _ _:

; . _ _6_ _ _ hi;_ _ _ _ 6_ _, _,z,= , bye, 6 J _,

; '' ,' ' 757='=

' ' / / / / ' ' 'g , ' / z / / / z , ' , ' ,> , ' ,,' , ' ,.

/ / / /. A , , ' , .

) ..

t,, ,,

IS - ---- - - - - - - - - - - - -- - -e - - - - - - - - -- - - ::Xt 4 - -t

Fig. 19. A series of simplified (xt) timing diagrams. In eachcase time is plotted horizontally and distance along the beamdirection is plotted vertically; the slope of an inclined line isproportional to the velocity of the corresponding neutrons. Thesymbols 1, 2, 3, and 4 represent the positions of choppers orchopper pairs; S and D represent the sample position and thedetector position, respectively. Breaks in horizontal lines repre-sent time periods when choppers are open to the passage ofneutrons. At (a) is shown an idealized timing diagram for asystem of two choppers. A more realistic timing diagram for thesame system (with counter-rotating choppers) is shown at (b).Several different neutron wavelengths are transmitted and someof those associated with one of the bursts are shown as heavylines. To stop the unwanted wavelengths order removal chop-pers are added, as shown at (c). Ambiguities in the analysis oftime-of-flight data can arise if the number of bursts at the sam-ple position is too high. This is illustrated at (d); one set ofneutrons which arrives at the detector at the same time is shownas heavy lines. A frame removal chopper is used to resolve theproblem, as shown at (e); in this example every third burst istransmitted.

so the intensity per pulse, at constant burst time, isproportional to the chopping speed of the system. Afurther advantage of the counter-rotating chopperpair concept, the possibility of using slots of differ-ent widths to enhance the resolution capabilities ofthe instrument [29], is discussed in Sec. 4.2. Thetiming diagram for two counter-rotating chopperpairs is essentially of the type illustrated in Fig.19(a).

Up to now we have glossed over the fact that neu-trons of more than one wavelength can be transmit-ted by systems such as those shown in Figs. 18(a)and 18(b); this possibility is illustrated in Fig. 19(b).Neutrons of the desired wavelength (Ao) take acertain time (which is proportional to Ao) to travelthe distance between the choppers. Neutrons whichtake an integral number of chopper periods longer(or shorter) than this time to travel the samedistance stand an equal chance of being transmit-ted. To suppress such neutrons we have determined

(a) W

U -_

I(t)

( b) /1_-W

-w wU U

Fig. 20. A linear chopping device is illustrated at (a); thewidths of the slot and the guide are both w and the choppingspeed is u. The time dependence of the transmitted intensity isshown at (b). The burst time is (w/u) whereas the transmittedintensity is proportional to (w 2 /u).

86

(a)4

XT

(b)1

(B1)

------------ 7____



that two additional "order removal" choppers arerequired. These choppers are placed at intermedi-ate locations between the pulsing and monochro-mating choppers as shown in Figs. 18(c) and 19(c);their exact positions are critical in order to removeall orders with intensity above background, underall conceivable operating conditions of the instru-ment.

The six choppers so far described collectively pro-duce sharp bursts of neutrons of a single well de-fined energy at the sample position, as in Fig. 19(c).From our previous discussion we have seen thatthese choppers should be operated at the highestacceptable speed in order to achieve the highestpossible intensity per pulse, but unfortunately theshortness of the time between pulses can introduceambiguities into the analysis of a TOF measure-ment. This is illustrated in Fig. 19(d). We see thatneutrons which arrive at the detector at a given timecan in general be associated with more than onepulse arrival time at the sample. On physicalgrounds it is generally possible to rule out all but afew possible energy transfers, but ambiguities maystill remain, in which case the appropriate course ofaction is to reduce the number of pulses at the sam-ple. This is achieved using a chopper which rotateswith a period that is an exact multiple of the periodof the other choppers. The net effect is illustratedin Fig. 19(e). In the DCS the frame overlap chopperis placed close to the first order removal chopper, asshown in Fig. 18(d), and in Fig. 15.

Acknowledgments

Our thanks to Jack Rush for his advice and en-couragement. We are grateful to Al Heald and LewRobeson for their help in creating several of thefigures in this paper, and to David Mildner for anumber of comments.

9. References[1] J. R. Dunning, G. B. Pegram, G. A. Fink, D. P. Mitchell,

and E. Segr6, Phys. Rev. 48, 704 (1935). See also G. A.Fink, Phys. Rev. 50, 738 (1936).

[2] E. Fermi, J. Marshall, and L. Marshall, Phys. Rev. 72, 193(1947).

[3] R. M. Brugger, Thermal Neutron Scattering, P. A.Egelstaff, ed., Academic Press, London and New York(1965), p. 53.

[4] M. Bee, Quasielastic Neutron Scattering: Principles andApplications in Solid State Chemistry, Biology and Mate-rials Science, Adam Hilger, Bristol and Philadelphia(1988).

[5] C. G. Windsor, Pulsed Neutron Scattering, Taylor andFrancis, London (1981).

[6] S. F. Trevino, J. Res. Natd. Inst. Stand. Technol. 98, 59(1993).

[7] D. A. Neumann and B. Hammouda, J. Res. Natl. Inst.Stand. Technol. 98, 79 (1993).

[8] N. F. Berk, J. Res. Natd. Inst. Stand. Technol. 98, 15(1993).

[9] J. J. Rush and J. M. Rowe, Physica 137B, 169 (1986).[10] R. R. Cavanagh, J. J. Rush, and R. D. Kelley, in Vibra-

tional Spectroscopy of Molecules on Surfaces, J. T. Yates,Jr., and T. E. Madey, eds., Plenum, New York (1987)p. 183.

[11] T. J. Udovic, D. A. Neumann, J. J. Rush, L. C. Sander, andI. S. Anderson, NIST Technical Note 1272, C. O'Connor,ed., U.S. Government Printing Office, Washington (1989)p. 1.

[12] R. Vacher, E. Courtens, G. Coddens, A. Heidemann, Y.Tsujimi, J. Pelous, and M. Foret, Phys. Rev. Lett. 65,1008 (1990).

[13] S. Feng, Phys. Rev. B 32, 5793 (1985).[14] W.-H. Li, J. W. Lynn, H. B. Stanley, T. J. Udovic, R. N.

Shelton, and P. Klavins, Phys. Rev. B 39, 4119 (1989).[15] T. M. Giebultowicz, P. Klosowski, J. J. Rhyne, T. J.

Udovic, J. K. Furdyna, and W. Giriat, Phys. Rev. B 41, 504(1990).

[16] A. Lewicki, A. I. Schindler, J. K. Furdyna, and W. Giriat,Phys. Rev. B 40, 2379 (1989).

[17] J. M. Nicol, J. Eckert, and J. Howard, J. Phys. Chem. 92,7117 (1988).

[18] A. Heidemann, K. J. Lushington, J. A. Morrison, K. Neu-maier, and W. J. Press, Chem. Phys. 81, 5799 (1984).

[19] I. S. Anderson, N. F. Berk, J. J. Rush, T. J. Udovic, R. G.Barnes, A. Magerl, and D. Richter, Phys. Rev. Lett. 65,1439 (1990).

[20] J. Kondo, Physica (Amsterdam) 125B, 279 (1984); 126B,377 (1984); 141B, 305 (1986).

[21] A. Magerl, A. J. Dianoux, H. Wipf, K. Neumaier, and I. S.Anderson, Phys. Rev. Lett. 56, 159 (1986).

[22] D. Steinbinder, H. Wipf, A. Magerl, D. Richter, A. J.Dianoux, and K. Neumaier, Europhys. Lett. 6, 535 (1988).

[23] H. Jobic, M. Bee, and A. Renouprez, Surface Sci. 140, 307(1984).

[24] H. Jobic, M. Bee, and G. J. Kearley, Zeolites 9, 312 (1989).[25] H. J. Prask, J. M. Rowe, J. J. Rush, and I. G. Schr6der, J.

Res. Natl. Inst. Stand. Technol. 98, 1 (1993).[26] J. R. D. Copley, Nucl. Instr. Meth. A 291, 519 (1990).[27] J. R. D. Copley, Nucl. Instr. Meth. A 303, 332 (1991).[28] J. R. D. Copley, Physica B 180 & 181, 914 (1992).[29] R. E. Lechner, Physica B 180 & 181, 973 (1992).[30] R. J. Royston, Nucl. Instr. Meth. 30, 184 (1964).[31] E. R. Cohen and B. N. Taylor, J. Res. Natd. Bur. Stand.

(U.S.) 92, 85 (1987).[32] J. R. D. Copley, Nucl. Instr. Meth. A 273, 67 (1988).

About the authors: John R. D. Copley and TerrenceJ. Udovic are scientists in the Reactor Radiation Divi-sion of the NIST Materials Science and EngineeringLaboratory. The National Institute of Standards andTechnology is an agency of the Technology Adminis-tration, U.S. Department of Commerce.

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Neutron Time-of-Flight Spectroscopy · The neutron time-of-flight technique has a long and distinguished history. In 1935, only 3 years ... used by Enrico Fermi and his collaborators